39.2.9 problem Problem 11.52

Internal problem ID [6526]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.52
Date solved : Monday, January 27, 2025 at 02:11:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=1+{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)+1,y(x), singsol=all)
 

\[ y = -1+\frac {\left (6 c_3 \,x^{2}+x^{3}+6 c_2 x +6 c_1 \right ) {\mathrm e}^{x}}{6} \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 31

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==Exp[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -1+e^x \left (\frac {x^3}{6}+c_3 x^2+c_2 x+c_1\right ) \]